Electron paramagnetic resonance dosimeter, methods of manufacture, and methods of use

ABSTRACT

A carbonated hydroxyapatite cement (CHC) precursor composition for an electron paramagnetic resonance dosimeter includes a cement powder and a cement liquid in a powder/liquid ration of 0.5 to 5. The includes one or more phosphate compounds selected from a group of monocalcium phosphate anhydrous, monocalcium phosphate monohydrate, dicalcium phosphate anhydrous, dicalcium phosphate dihydrate, amorphous calcium phosphate, α-tricalcium phosphate, β-tricalcium phosphate, and tetracalcium phosphate. The cement liquid is an aqueous phosphate solution having a total phosphate concentration in a range of 0.005 to 2.4 moles per liter (mol/L).

RELATED APPLICATIONS

This patent application is a continuation of U.S. patent applicationSer. No. 16/431,872 filed Jun. 5, 2019, entitled “Electron ParamagneticResonance Dosimeter, Methods of Manufacture, and Methods of Use,” whichis a division of U.S. patent application Ser. No. 15/068,943 filed Mar.14, 2016, entitled “Electron Paramagnetic Resonance Dosimeter, Methodsof Manufacture, and Methods of Use,” now U.S. Pat. No. 10,509,092,issued Dec. 17, 2019, which claims priority to provisional patentapplication 62/133,018 filed Mar. 13, 2015, entitled “ElectronParamagnetic Dosimeter, Dosimetry Reference, Methods of Manufacture, andMethods of Use.” The disclosures of these applications and the patentare incorporated by reference.

BACKGROUND

Certain materials, when exposed to ionizing radiation, can be stimulatedto emit a measurable signal that may be used to estimate the receivedradiation dose. Certain of these materials may be incorporated into adosimeter that is worn or carried by an individual to measure theindividual's exposure. A thermoluminescent dosimeter (TLD) is anexample. To be effective in monitoring radiation exposure, the TLD mustbe worn or carried by the individual during periods of possibleradiation exposure. For medical/industrial applications of ionizingradiation, dosimeters are used to assess the quality of the treatment orprocess.

Dosimetry systems and techniques exist that exploit radiation-inducedsignals emanating from biological materials. In some of thesetechniques, the signals may be measured in vivo. Examples of suchtechniques include electron paramagnetic resonance (EPR) dosimetry,which may be used to measure signals in teeth, fingernails, toenails,bone and hair. These techniques hold out the promise for screening(i.e., as part of a triage effort), at a point-of-care facility, largepopulations groups that may have been exposed to ionizing radiation.

EPR dosimetry is based on the following: (1) ionizing radiationgenerates unpaired electrons (e.g., free radicals) in proportion to theabsorbed dose; (2) EPR dosimetry can selectively and sensitively detectand determine the number of unpaired electrons; and (3) the unpairedelectrons can persist in some tissues, such as teeth and nails, withenough stability so as to be measured by EPR dosimetry weeks to yearsafter radiation exposure.

SUMMARY

A dosimeter for EPR dosimetry systems includes a carbonatedhydroxyapatite cement formed by mixing a cement powder and a cementliquid in a ratio of a range of about 0.5 to 5.0 powder-to-liquid ratio.The cement powder comprises one or more calcium phosphate compounds andone or more carbonate compounds. The cement liquid comprises a phosphatesolution. The cement, when irradiated by a radiation source, is capableof producing a measurable signal comprising a spectrally clean EPRspectrum. Furthermore, the measurable signal is proportional to thereceived radiation dose.

An electron paramagnetic resonance (EPR) device includes a crystalline,emission-sensitive mass and a housing containing the device. The massincludes structurally incorporated carbonate content in a range of about3% by weight to about 10% by weight of the mass, one or morestructurally incorporated non-calcium metallic cations, and one or morestructurally incorporated phosphate anions. When irradiated with a knownsource, the EPR device may function as a reference. When unirradiated,the EPR may function as a dosimeter. As a dosimeter, the EPR device maybe used as a personal dosimeter or as a monitor for inanimate objectsbeing subjected to radiation sources. The EPR dosimeter may be used forboth gamma radiation and neutron radiation measurements.

DESCRIPTION OF THE DRAWINGS

The Detailed Description refers to the following Figures, in which likenumerals refer to like items, and in which:

FIG. 1 is a simplified block diagram of an example EPR dosimetry system;

FIG. 2 illustrates examples of carbonated hydroxyapatite cement samplesfor the EPR dosimetry system of FIG. 1;

FIG. 3 illustrates XRD patterns of carbonated hydroxyapatite sampleswith different carbonate content;

FIG. 4 illustrates FTIR patterns of carbonated hydroxyapatite cementsamples with 3% and 10% carbonate contents;

FIG. 5 illustrates an EPR spectrum of carbonated a hydroxyapatite cementsample with 3% carbonate content;

FIG. 6 illustrates an example use of EPR dosimetry using a carbonatedhydroxyapatite dosimeter; and

FIG. 7 illustrates carbonated hydroxyapatite used as a reference sourcefor EPR dosimetry.

DETAILED DESCRIPTION

Disclosed herein a dosimeter that uses a novel material to captureionizing radiation and provide for reliable measurement of receiveddose. Also disclosed are methods of manufacture and methods of use. Thedosimeter is based on the following concepts developed by the inventorsto this application:

-   -   A carbonated hydroxyapatite cement (CHC) may serve as an        inexpensive, easily formed material for the dosimeter.    -   For a given crystallinity of the CHC material, the EPR signal        produced by a given irradiation dose increases with increasing        carbonate content in the apatite.    -   For a given carbonate content, the EPR signal produced by a        given irradiation dose decreases with decreasing crystallinity        of the CHC material.    -   For a given crystallinity and carbonate content, the EPR signal        increases with the absorbed radiation dose.    -   The crystallinity of CHC decreases with increasing carbonate        content.    -   For a given carbonate content, the crystallinity increases,        within certain limits, with increasing calcium substitution by        sodium.

Starting with these hypotheses, the inventors developed severalself-hardening cement compositions, and subjected the compositions tovarious tests, described herein, to prove these hypotheses.

In the course of this analysis and testing, the inventors discoveredother surprising and unexpected properties and hence uses for the cementcompositions. These other properties and uses are disclosed herein.

In the course of the investigations, the inventors discovered thatcertain of these cement compositions could function well as an EPRdosimeter. More specifically, and in a herein described embodiment, theEPR dosimeter is based on the surprising discovery that a specialsynthetic carbonated hydroxyapatite cement (CHC) material in the form ofa hardened mass of any desired dimension may, when exposed to certainionizing radiation, produce an EPR signal. These materials are pure CHCwithout any binders. The materials may be in the shape of a cylinder,disc, block, plate, or film. Further, the CHC samples are chemicallystable and have adequate mechanical strength and surface integrity to beused for any EPR dosimetry system.

In addition, the CHC compositions may have the potential to be used withother than photon irradiation, including irradiation from neutronsources.

The novel CHC precursor compositions include cement powder that consistsof one or more calcium phosphate compounds selected from a group thatincludes monocalcium phosphate anhydrous, monocalcium phosphatemonohydrate, dicalcium phosphate anhydrous, dicalcium phosphatedihydrate, amorphous calcium phosphate, α-tricalcium phosphate,β-tricalcium phosphate, and tetracalcium phosphate.

The compositions further include one or more soluble carbonate compounds(such as sodium carbonate, sodium bicarbonate, potassium carbonate,potassium bicarbonate, ammonium carbonate) or sparingly solublecarbonate compounds (such as calcium carbonate, iron carbonate,magnesium carbonate, and zinc carbonate).

Optionally, the cement powder also may include one or more of thefollowing;

-   -   Sparingly soluble calcium compounds (such as calcium lactate,        calcium sulfate, calcium oxide, and calcium hydroxide).    -   Sparingly soluble phosphate compounds (such as iron phosphate,        magnesium phosphate, zinc phosphate).    -   Soluble phosphate compounds (such as sodium phosphate and        potassium phosphate).    -   One or more water reducing agents such as sodium citrate and        citric acid.    -   Median particle sizes of each of the cement powder components        should be in the range of 0.1 to 150 μm.    -   Cement liquid in an aqueous phosphate solution with total        phosphate concentration in the range of about 0.005 to 2.5        mol/L. The liquid may further contain gelling agents such as        cellulose and a water reducing agent such as citrate.

Samples of the cement compositions were prepared according to thefollowing:

-   -   The cement powder and liquid were mixed with a powder/liquid        ratio in the range of about 0.5 to 5 to produce a uniform paste.    -   The paste was then placed in a mold of desired shape and        dimensions.    -   After one day, the hardened sample was removed from the mold.        The demolded sample was immersed in a physiological-like fluid        for 5 days to allow the cement setting reaction to complete.        Optionally, the formed sample can be fired to produce a ceramic        material with enhanced properties.

A fully set CHC sample is an impure hydroxyapatite with a low to mediumcrystallinity compared to pure hydroxyapatite (NIST standard referencematerial). The material contains a structurally incorporated carbonatecontent in the range of 0.05 to 12 mass %. The material also may containstructurally incorporated non-calcium metallic cations (such as Na⁺) andacid phosphate anion, HPO₄ ²⁻.

Example 1

In Example 1, a cement powder consisted of tetracalcium phosphate,dicalcium phosphate, and sodium bicarbonate to allow the CHC product tocontain 3% by weight of carbonate. The cement liquid was 0.5 mol/LNa₂HPO₄ solution. Cement paste with a powder/liquid ratio of 3 wasprepared and placed in a mold to produce discs (6 mm D×3 mm H). Thehardened discs were analyzed by XRD and FTIR for phase composition andcarbonate contents, respectively. The CHC discs were then gamma-rayirradiated to 10 kGy (10,000 Gy) with a NIST-calibrated Co-60 source andtheir EPR characteristics were determined.

XRD showed that the only phase present in hardened CHC samples was lowcrystalline HA. FTIR analysis revealed carbonate bands at 1413 cm⁻¹ and1455 cm⁻¹ indicating that the HA contained type-b carbonate similar tothe carbonate in apatitic biometerials. After gamma-ray irradiation, theCHC discs showed reproducible EPR signals. The 3% carbonate samplesexhibited a spectrally perfect example of the radical.

Example 2

In Example 2, the materials were as described in example 1, except thatthe carbonate content was increased to 10% by weight. The materials wereformed into hardened discs and the discs were subjected to the sametesting as described for Example 1. The 10% carbonate sample alsoproduced EPR signals. However, the signals are not spectrally clean(FIG. 5 illustrates a spectrally clean EPR signal), making the materialless suitable for use as high accuracy dosimeters or dosimeter referencesources.

The following table illustrates additional potential components of acarbonated hydroxyapatite cement.

TABLE Cement Powder Expected Product Cement Liquid Ca₄(PO₄)₂O + CaHPO₄ +NaHCO₃ Ca_(5−x)Na_(x)(PO₄)_(3−x)(CO₃)_(x)OH Na₂HPO₄ solutionCa₄(PO₄)₂O + CaHPO₄ + KHCO₃ Ca_(5−x)H_(x)(PO₄)_(3−x)(CO₃)_(x)OH K₂HPO₄solution 3CaHPO₄ + 2CaCO₃ + NaFCa_(5−x)Na_(x)(PO₄)_(3−x)(CO₃)_(x)OH_(1−y)F_(y) Na₂HPO₄ solution3CaHPO₄ + 2CaCO₃ + KF Ca_(5−x)H_(x)(PO₄)_(3−x)(CO₃)_(x)OH_(1−y)F_(y)K₂HPO₄ solution

Rather than forming a cement (i.e., CHC), the carbonated hydroxyapatitepowder, as noted herein, may be fired or sintered to form a hardenedmass, which in turn, may serve as a component of an EPR dosimeter or asan EPR reference source.

FIG. 1 is a simplified diagram of an example CH-based EPR dosimetrysystem. In FIG. 1, EPR dosimetry system 10 includes EPR dosimeter 20,dosimeter reader 30, and reference source 40. The EPR dosimeter 20includes carbonated hydroxyapatite cement (CHC) material 22 thatreceives a radiation dose and, when read in an appropriate dosimeterreader produces a measurable signal such as those shown in FIG. 4. Asdisclosed herein, the CHC material 22 is a carbonated hydroxyapatitecement formulated as described in Examples 1 and 2. The CHC material 22may be enclosed in structure or housing 24 that protects the materialand that allows the dosimeter 20 to be effectively attached to object 50whose cumulative radiation dose is to be monitored and measured. Forexample, the structure 24 may include a clip 26 that enables thedosimeter 20 to be attached to the clothing of a human subject. FIG. 6,described later, illustrates other structures for enclosing, protecting,and attaching an EPR dosimeter to an object whose cumulative radiationdose is to be monitored.

FIG. 2 illustrates an example of carbonated hydroxyapatite cementreference source samples for the EPR dosimetry system of FIG. 1. In FIG.2, three different CHC references sources are shown. A first disc has adiameter of 6 mm and a thickness 2 mm; a second disc has a diameter of 6mm and a thickness of 4 mm; and a third disc has a diameter of 6 mm anda thickness of 12 mm.

FIG. 3 illustrates XRD patterns of carbonated hydroxyapatite sampleswith different carbonate content. In FIG. 3, XRD patterns are shown fora CH powder produced, for example, by precipitation (the lowest curve inFIG. 3) and, respectively, a CHC sample with 10% carbonate, a CHC samplewith 3% carbonate, and a CHC sample with 0% carbonate. The XRD patternsshow that all the CHC samples and the CH powder contain low crystallinehydroxyapatite with no unreacted cement or other impurities.

FIG. 4 illustrates FTIR patterns that show that the CHC samples werehydroxyapatite that contained two levels of type-b carbonate similar toapatitic biominerals.

FIG. 5 illustrates an EPR spectrum of a carbonated hydroxyapatite cementreference source sample with 3% carbonate content. As can be seen, theCHC with 3% carbonate produced a spectrally clean example of theradical. The spectrum is free of paramagnetic impurities that wereobserved in CH powder.

The herein disclosed carbonated hydroxyapatite cements may be used in adosimeter for the measurement of ionizing radiation absorbed dose. Inthis situation, the dosimeters may be uniformly mass-produced in a sizeand shape and shipped to an end user, unirradiated. The dosimeters maybe packaged (for example, in a blister pack) and may each be provided aunique identification, such as a bar code or other optical orradiofrequency readout device. The dosimeters may incorporate the hereindisclosed cement compositions in a variety of shapes and sizes toaddress a specific measurement need. Though not a requirement, theaddition of a binder may be employed to fabricate a dosimeter of adesired shape for use in a specific application. Such shapes includecylinders (see, for example, FIG. 2), films (either rigid or flexible),or a custom shape or coating to accommodate a specific need.

In an embodiment, such dosimeters may be issued to individuals to serveas personal dosimeters (see FIG. 1).

In another embodiment, such dosimeters may be attached to containers ofraw materials (e.g., shrink-wrap films) and/or finished products (e.g.,foods or medical devices) that are to receive a high radiation dose withthe intent of achieving a desirable effect (e.g., destruction oftoxins/microorganisms, or modification of the material's physicalproperties). After such exposure, the dosimeters are removed andprocessed using an EPR spectroscopy system to verify the article orpackage to be irradiated did in fact receive an absorbed radiation dosewithin the targeted range. As a more specific example, the packaged andidentified dosimeters may be attached to containers on a conveyor systemthat moves the containers past an irradiation source that could be aradioisotope (e.g., Co-60) or an electron beam accelerator of energiesbetween 50 keV and 10 MeV.

FIG. 6 illustrates an exemplary embodiment of the herein disclosedcarbonated hydroxyapatite cement (CHC) used as a dosimeter. In FIG. 6,system 600 includes transfer assembly 611, which is used to movepackages 601 past radiation source 630. One or more of the packages 601may have affixed thereon, CHC dosimeter 621, which is packaged inblister pack 620. The CHC dosimeter may be supported on a substrate. Thesubstrate may be imprinted with identification device 623. Theidentification device may be a barcode, for example.

In another embodiment, by incorporation of sensitizers, the cementcompositions may be adapted for a specific dose range (high range forindustrial applications; low range for personal dosimetry) or a specifictype of ionizing radiation (e.g., neutron radiation). In addition, thecement compositions may incorporate paramagnetic reference materials toimprove the accuracy and precision of the absorbed dose measurement.

EPR Biodosimetry with Irradiated CHC as a Reference Source

A large-scale radiation event such as a reactor accident or explosion ofa nuclear device has the potential to expose a large population toionizing radiation. Some members of this population may be minimallyexposed and need little if any medical treatment; others may receive alarger exposure, and may require medical treatment; still others mayhave received so large a dose that medical treatment may not sufficient.Medical emergency response personnel may conduct a triage operation inan effort to identify and adequately treat the maximum number of exposedpersonnel. Unfortunately, since the population members likely are notbeing monitored with supplied individual dosimetry, current triagemethods may rely on clinical procedures, which may not be able to handlethe throughput necessary to assess the entire population. For example,clinical methods may require sample analysis at a remote facility, whichin turn may require sample transport and later matching of sampleresults with the individuals. Alternately, or in addition to clinicalanalysis, triage methods may rely on field analysis that accessescertain symptoms. These field methods may be very inaccurate. Thus,current triage methods cannot be effectively employed when perhaps manythousands of persons must be evaluated and medical decisions madequickly.

An alternative to current triage methods involves use of biodosimetry.Biodosimetry does not rely on an individual carrying or being in closeproximity to a dosimeter. Rather, biodosimetry relies on the fact thatcertain portions of the human body, when exposed to certain ionizingradiation, can give off a measurable signal that indicates suchexposure. Determining or estimating radiation exposure in the case ofbiodosimetry may rely on electron paramagnetic resonance (EPR). Suchresonance provides signals that may be read by a suitable EPRspectrometer.

EPR spectroscopy is a non-destructive technique that may be used todetect and quantify unpaired electrons (e.g., free radicals). Theunpaired electrons result from the absorption of ionizing radiation in atarget material.

Thus, to determine if an individual has been exposed to ionizingradiation, a device or system such as an EPR spectrometer-based systemmay be used, in vivo. For example, to determine if a person was exposedto ionizing radiation, as indicated by production of free radicals inthe person's teeth, the system may include resonators that are attachedto a tooth. The resonators are coupled to a magnet system thateffectively encompasses the subject's head.

Dose determination using electron paramagnetic resonance (EPR)spectroscopy of human tooth enamel (EPR biodosimetry) is an establishedtechnique for dose reconstruction in radiation accidents during photonirradiation. This technology is based on the fact that ionizingradiation generates unpaired electrons proportional to dose and that, intooth enamel, these unpaired electron species are extremely stable,persisting for thousands of years. To use this technology, the EPRbiodosimeter needs to be calibrated using a set of references thatexhibit known and reproducible EPR signals in the desired range.Although tooth enamel is capable of exhibiting stable EPR signalsproportional to the ionization irradiation dose, it is not an idealreference tool for numerous reasons including its non-uniform chemicalcomposition, variable physical properties, and unknown radiationhistory.

One aspect of EPR dosimetry that remains unresolved is the developmentand deployment of suitable reference sources for EPR dosimetry readers(i.e., EPR spectrometers). If available, such reference sources could beused to verify proper operation of the EPR spectrometers. To improve EPRdosimetry, especially to improve the integrity of a field-deployed EPRbiodosimetry system that determines exposure to population members,disclosed herein is an EPR reference source, method of manufacture, andmethod of use.

FIG. 7 is a block diagram of an alternate EPR dosimetry system. In FIG.7, EPR dosimetry system 700 includes dosimeter reader 710, which in turnincludes power supply 711, EPR electronics 713, user interface 715,processor 717, and measurement unit 719. The measurement unit 719 mayinclude a resonator (not shown) that contacts one or more teeth ofpatient 730. The measurement unit 719 includes a magnet coil section 718which provides the required magnetic field to induce an EPR signal.

Also shown in FIG. 7 is a reference source 720, which is used to confirmproper operation of the system 710.

In operation, the EPR system 710 may be field-deployed to perform triageoperations following a large-scale radiation event. FIG. 7 illustratesone possible configuration of an EPR measurement unit 719. In thisconfiguration the patient's head may be surrounded by, or merelyadjacent a set of magnet coils that induce the magnetic field necessaryto generate an EPR signal.

The reference source 720 is used to perform an initial check of thesystem 710, and may thereafter be used to periodically confirm properoperation of the system 710. The reference source 720 may have a formdictated by the system 710. For example, the reference source 720 mayhave any of the forms shown in FIG. 2.

Prior to shipment to the operator of system 710, the reference source720 may be irradiated. For example, a certified laboratory may irradiatethe reference source 720 using a Co-60 source. After such irradiation,and prior to shipment, the reference source 720 may be tested in thelaboratory to verify that it provides the desired EPR signal.

Disclosed above are methods (self-setting cement, sintering) forproducing the carbonated hydroxyapatite (CH) crystalline structure usedin an example EPR dosimeter. Other methods, including use of otherstarting components, also may produce a satisfactory crystallinestructure for an EPR dosimeter. In particular, methods that result insubstantially complete CH formation may be used to produce asatisfactory crystalline structure. In particular, U.S. Pat. No.5,525,148, incorporated herein by reference, discloses methods forforming a hardened CH mass,

In addition to the self-setting cement forming processes describedabove, a satisfactory carbonate-substituted hydroxyapatite material maybe formed by non-cement processes such as those disclosed in thefollowing, which are hereby incorporated by reference:

-   1. L. G. Ellies, D. G. A. Nelson, J. D. B. Featherstone (1988):    Crystallographic structure and surface morphology of sintered    carbonated apatites. Journal of Biomedical Materials Research,    Volume 22, Issue 6, pages 541-553.-   2. lain R. Gibson and William Bonfield (2002): Novel synthesis and    characterization of an AB-type carbonate-substituted hydroxyapatite.    Journal of Biomedical Materials Research, Volume 59, Issue 4, pages    697-708.-   3. T. S Sampath Kumara, I Manjubalaa, J Gunasekarana (2000):    Synthesis of carbonated calcium phosphate ceramics using microwave    irradiation. Biomaterials, Volume 21, Issue 16, August 2000, Pages    1623-1629.-   4. J. P. Lafona, E. Championa, D. Bernache-Assollantb (2008):    Processing of AB-type carbonated hydroxyapatite    Ca10-x(PO4)6-x(CO3)x(OH)2-x-2y(CO3)y ceramics with controlled    composition. Journal of the European Ceramic Society, Volume 28,    Issue 1, Pages 139-147.-   5. Michael E. Fleet, Xi Liu (2007): Coupled substitution of type A    and B carbonate in sodium-bearing apatite. Biomaterials, Volume 28,    Issue 6, Pages 916-926.

We claim:
 1. A carbonated hydroxyapatite cement (CHC) precursorcomposition for an electron paramagnetic resonance dosimeter,comprising: a cement powder comprising one or more phosphate compoundsselected from a group consisting of monocalcium phosphate anhydrous,monocalcium phosphate monohydrate, dicalcium phosphate anhydrous,dicalcium phosphate dihydrate, amorphous calcium phosphate, α-tricalciumphosphate, β-tricalcium phosphate, and tetracalcium phosphate; a cementliquid comprising an aqueous phosphate solution having a total phosphateconcentration in a range of 0.005 to 2.4 moles per liter (mol/L); andthe cement powder and the cement liquid in a powder/liquid ratio in arange of 0.5 to
 5. 2. The precursor composition of claim 1, the cementpowder further comprising one or more soluble carbonate compoundsselected from a group consisting of sodium carbonate, sodiumbicarbonate, potassium carbonate, potassium bicarbonate, ammoniumcarbonate, and ammonium bicarbonate.
 3. The precursor composition ofclaim 1, the cement powder further comprising one or more sparinglysoluble carbonate compounds selected from a group consisting of calciumcarbonate, iron carbonate, magnesium carbonate, and zinc carbonate. 4.The precursor composition of claim 1, the cement powder furthercomprising one or more sparingly soluble calcium compounds selected froma group consisting of calcium lactate, calcium sulfate, calcium oxide,and calcium hydroxide.
 5. The precursor composition of claim 1, thecement powder further comprising one or more sparingly soluble phosphatecompounds selected from a group consisting of iron phosphate, magnesiumphosphate, and zinc phosphate.
 6. The precursor composition of claim 1,the cement liquid further comprising one or more gelling agents and oneor more water reducing agents.
 7. The precursor composition of claim 1,wherein the cement powder comprises 3% to 10% by weight of carbonate. 8.The precursor composition of claim 1, the cement powder furthercomprising one or more of sodium fluoride and potassium fluoride.
 9. Aprecursor composition for an electronic paramagnetic resonancedosimeter, comprising: a powder comprising one or more phosphatecompounds selected from a group consisting of monocalcium phosphateanhydrous, monocalcium phosphate monohydrate, dicalcium phosphateanhydrous, dicalcium phosphate dihydrate, amorphous calcium phosphate,α-tricalcium phosphate, β-tricalcium phosphate, and tetracalciumphosphate; and the precursor composition comprises 3% to 10% by weightof carbonate.
 10. The precursor composition of claim 9, wherein theprecursor composition is sintered to form a hardened mass.
 11. Theprecursor composition of claim 9, further comprising one or morecarbonate compounds selected from a group consisting of sodiumcarbonate, sodium bicarbonate, potassium carbonate, potassiumbicarbonate, ammonium carbonate, and ammonium bicarbonate.